In part $($a$)-($c$)$ determine if the following signatures are good or bad:

a$.N=13962799$ and $e=3$ value to sign $m=821$ and signature $=8674413$

b$.N=34300129$ and $e=61$ value to sign $m=2478$ and signature $=27535246$

c$.N=5898461$ and $e=23$ value to sign $m=419$ and signature $=2607727$

d$.$ Suppose that you have an RSA modulus with prime factors $p=3181$ and $q=2677$ and the public exponent is $163.$ Calculate

the signature of $521$ and then verify it$.$